Question
Answer
$$\dfrac{15x^3+60x^2-75x}{9x^2+66x+105}=\dfrac{5x^2-5x}{3x+7}$$
Explanation
| $$ \begin{aligned}\frac{15x^3+60x^2-75x}{9x^2+66x+105}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5x^2-5x}{3x+7}\end{aligned} $$ | |
| ① | Simplify $ \dfrac{15x^3+60x^2-75x}{9x^2+66x+105} $ to $ \dfrac{5x^2-5x}{3x+7} $. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{3x+15}$. $$ \begin{aligned} \frac{15x^3+60x^2-75x}{9x^2+66x+105} & =\frac{ \left( 5x^2-5x \right) \cdot \color{blue}{ \left( 3x+15 \right) }}{ \left( 3x+7 \right) \cdot \color{blue}{ \left( 3x+15 \right) }} = \\[1ex] &= \frac{5x^2-5x}{3x+7} \end{aligned} $$ |
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